The striker headed in his second goal of the afternoon in the dying stages following a goalmouth scramble.
Paul Heffernan thought he had netted the winner for Hibs in the 79th minute as the home side responded to going two down after just 29 minutes.
Sutton opened the scoring before Lionel Ainsworth notched a brilliant individual effort.
Jordan Forster gave the hosts hope moments before the break with a headed effort and Michael Nelson levelled in the second half with a contentious effort that referee Steven McLean adjudged to have crossed the line.
Hibs started this thrilling contest brightly but fell behind in the 12th minute against the run of play.
James McFadden played in Ainsworth, down the left flank and the forward's low pass across goal was placed into the net by the unmarked Sutton at the back post.
Hibs had a chance to test Lee Hollis after 20 minutes when the Motherwell goalkeeper could only partially clear a backpass.
Paul Cairney picked up the ball on the edge of the box and found Danny Haynes after Stephen McManus failed to cut out the delivery - but Haynes shot over on the half-volley 15 yards from goal.
Motherwell doubled their advantaged in the 29th minute with a brilliant individual effort from Ainsworth.
The on loan Rotherham forward accepted a pass from Keith Lasley, effortlessly nutmegged Nelson and darted goalwards before curling a sublime 18-yard effort into the top corner of the net from 18 yards.
The visitors had looked comfortable but Hibs managed to reduce their arrears two minutes before the break through Forster.
Cairney's corner eventually came back to him and he lifted a delivery into the six-yard box that was headed in by the defender.
Hibs could have been level just seconds later but Hollis brilliantly turned a James Collins effort from 12 yards around the post.
The hosts started the second half brightly and created two good chances.
Collins curled a first-time effort off the post with the outside off his boot from a Ryan McGivern pass and could only bounce the rebound into the arms of the grounded Hollis.
Haynes then blasted over from an angle inside the area in the 49th minute after being set up inside the box by Cairney.
McFadden created a chance for himself after 72nd minutes, shooting wide from inside the area after driving past Sam Stanton and Paul Hanlon in a forceful run from midfield.
The home side levelled in the 76th minute in controversial circumstances.
Cairney's corner was met at a congested back post by Nelson and the defender's downward header bounced off the underside of the bar. Motherwell thought they had successfully cleared the danger but referee McLean awarded a goal.
Hibs stormed ahead in the 79th minute through Heffernan, just four minutes after he came on.
Heffernan began the counter-attack charge with a pass to Stanton inside his own half, Cairney drove at the Motherwell defence after being found by Stanton and teed up the substitute - who lifted a shot over Hollis.
The drama was not over there though, with Sutton earning the visitors a point with his second goal - in stoppage-time following a scramble inside the six-yard box.